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$If x, y, z \in ℝ^{+} such that x + y + z = 4, then maximum possible value of x y z^{2} is:$

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Correct option is D

Given that x+y+z=4x+y+z4=1Arithmetic meanA.M≥Geometric mean(G.M)x+y+z2+z24≥x.y.z2.z214⇒1≥xyz2414⇒xyz2≤4 Maximum value of xyz2 is 4

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If x,y,z∈ℝ+such that x+y+z=4, then maximum possible value of xyz2 is:

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$If x, y, z \in ℝ^{+} such that x + y + z = 4, then maximum possible value of x y z^{2} is:$